Parametric system for quantifying analyte polynucleotides

ABSTRACT

System for quantifying analyte polynucleotides employs computer-implemented analysis of real-time amplification data using a calibration curve defined by parametric equations.

RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.11/599,940, filed Nov. 14, 2006, now U.S. Pat. No. 7,831,417, whichclaims the benefit of U.S. Provisional Application No. 60/737,334, filedNov. 14, 2005. The entire disclosures of these prior applications arehereby incorporated by reference.

FIELD OF THE INVENTION

The present invention relates to the field of biotechnology. Morespecifically, the invention relates to quantitation of analytepolynucleotides using nucleic acid amplification technology, and stillmore specifically relates to the use of internal calibrators thatcoamplify with analyte polynucleotides.

BACKGROUND OF THE INVENTION

Methods involving the kinetic analysis of in vitro nucleic acidamplification have become important tools for quantifying analytepolynucleotides. In these procedures, sometimes referred to as“real-time” amplification procedures, the amount of amplicon present ina nucleic acid amplification reaction mixture is monitored as a functionof time over the course of the amplification procedure. Fully automatedreal-time nucleic acid assays require machine executable algorithmscapable of analyzing the time-dependent data acquired during thereaction. In this regard, there is a requirement for data processingalgorithms that accurately output an amount or concentration of anucleic acid that would give rise to an observed amplification result.

Difficulties associated with quantifying the absolute amount of aspecific nucleic acid target have been appreciated in the patentliterature. These difficulties have been attributed to the exponentialnature of the amplification process, and the fact that small differencesin any of the variables which control the reaction rate, including thelength and nucleotide sequence of the primer pairs, can lead to dramaticdifferences in amplicon yield. Wang et al., in U.S. Pat. No. 5,219,727described the use of an internal standard that amplified using the sameprimers that amplified the analyte polynucleotide, and addressed thefact that use of an unrelated cDNA as a standard necessitated a secondset of oligonucleotide primers unrelated to the specific target nucleicacid being quantified. According to Wang et al., analyses which use twosets of unrelated primers can only provide a relative comparison of twoindependent amplification reactions rather than an absolute measure of anucleic acid target concentration. Others have followed this teachingand employed internal standards that resemble the target of interest byhaving similar sequences, and by amplifying with a common pair ofprimers (see published U.S. patent application Ser. No. 10/230,489).Still others have described quantitative methods that rely ondetermining the efficiency of amplification (see published EuropeanPatent Application EP 1138784). Yet another approach has involveddetermining amplification ratios for control and target sequences (seeU.S. Pat. No. 6,066,458).

Notably, some prior quantitative algorithms that adjust for theefficiency of a coamplified species rely on rationally designedequations to estimate the behavior of a calibration curve over acritical range. As a result, these approaches may not fit theexperimental data over the full range of standards employed in aprocedure. Alternatively, the prior algorithms are best suited to aparticular amplification method, and so are not generally suitableacross different assay platforms.

The invention described herein addresses these deficiencies, and hasbeen shown to improve quantitation of analyte polynucleotides.

SUMMARY OF THE INVENTION

A first aspect of the invention relates to a method of preparing aparametric calibration curve for quantifying an analyte polynucleotidecontained in a test sample. In accordance with the method, first thereis a step for forming a plurality of standard samples, each containing aconstant quantity of a nucleic acid calibrator and a known startingquantity of an analyte polynucleotide standard. Next, there is a stepfor coamplifying the nucleic acid calibrator and the analytepolynucleotide standard in an in vitro nucleic acid amplificationreaction for each of the plurality of standard samples. Next, there is astep for determining indicia of amplification for the nucleic acidcalibrator and the analyte polynucleotide standard that coamplified ineach in vitro nucleic acid amplification reaction of the coamplifyingstep. This results in a collection of determined indicia ofamplification for the nucleic acid calibrator as a function of the knownstarting quantity of the analyte polynucleotide standard, and acollection of determined indicia of amplification for the analytepolynucleotide standard as a function of the known starting quantity ofthe analyte polynucleotide standard. Next, there is a step foroptimizing a first parametric equation to fit a first curve to thecollection of determined indicia of amplification for the nucleic acidcalibrator as a function of the known starting quantity of the analytepolynucleotide standard, thereby resulting in a first fitted equation.Next, there is a step for optimizing a second parametric equation to fita second curve to the collection of determined indicia of amplificationfor the analyte polynucleotide standard as a function of the knownstarting quantity of the analyte polynucleotide standard, therebyresulting in a second fitted equation. Next, there is a step for solvingthe first and second fitted equations at incremental values of the knownstarting quantity of the analyte polynucleotide standard to result in(a) fitted indicia of amplification for the nucleic acid calibrator as afunction of the known starting quantity of the analyte polynucleotidestandard, and (b) fitted indicia of amplification for the analytepolynucleotide standard as a function of the known starting quantity ofthe analyte polynucleotide standard. Finally, there is a step forpreparing a three-dimensional parametric calibration curve by relating:(a) fitted indicia of amplification for the analyte polynucleotidestandard as a function of the known starting quantity of the analytepolynucleotide standard in a first dimension; (b) fitted indicia ofamplification for the nucleic acid calibrator as a function of the knownstarting quantity of the analyte polynucleotide standard in a seconddimension; and (c) a function of the known starting quantity of theanalyte polynucleotide standard in a third dimension. In a preferredembodiment, the invented method further includes a step for projectingthe three-dimensional parametric calibration curve onto a measurementplane defined by the first and second dimensions, whereby there iscreated a two-dimensional calibration curve projection in themeasurement plane. When this is the case, the coamplifying step caninclude a procedure for amplifying the nucleic acid calibrator using afirst set of amplification oligonucleotides, and amplifying the analytepolynucleotide standard using a second set of amplificationoligonucleotides. In this instance, the first and second sets ofamplification oligonucleotides preferably are different from each other.Alternatively, the step for determining indicia of amplification caninvolve determining threshold-based indicia of amplification. Underanother alternative, the step for determining indicia of amplificationdoes not involve determining threshold-based indicia of amplification.Under still another alternative, each of the first and second fittedequations has four coefficients. In another preferred embodiment of theinvented method, the in vitro nucleic acid amplification reaction in thecoamplifying step is an isothermal in vitro nucleic acid amplificationreaction. For example, the isothermal in vitro nucleic acidamplification reaction can be a transcription-associated amplificationreaction. In a different preferred embodiment, when the invented methodincludes the step for projecting the three-dimensional parametriccalibration curve onto the measurement plane there are further includedsteps for (a) forming a test reaction mixture that includes the testsample and the constant quantity of the nucleic acid calibrator, (b)coamplifying in an in vitro nucleic acid test amplification reaction thenucleic acid calibrator and any analyte polynucleotide contained in thetest reaction mixture, and (c) determining indicia of amplification forthe nucleic acid calibrator and the analyte polynucleotide thatcoamplified in the in vitro nucleic acid test amplification reaction.More preferably, there is an additional step for quantifying the analytepolynucleotide contained in the test sample. Still more preferably, thequantifying step involves comparing the determined indicia ofamplification for the nucleic acid calibrator and the analytepolynucleotide that coamplified in the in vitro nucleic acid testamplification reaction with the two-dimensional calibration curveprojection in the measurement plane. Alternatively, the quantifying stepcan involve first specifying in the measurement plane a test sample datapoint having coordinates for the determined indicia of amplification forthe nucleic acid calibrator and the analyte polynucleotide thatcoamplified in the in vitro nucleic acid test amplification reaction,and then determining a value for a third dimension coordinate of thethree-dimensional parametric calibration curve that minimizes thedistance separating the test sample data point and a point on thetwo-dimensional calibration curve projection in the measurement plane.When this is the case, the step for determining the value for the thirddimension coordinate of the three-dimensional parametric calibrationcurve can involve calculating the length of a right triangle hypotenuse.Alternatively, the coamplifying step can involve amplifying the nucleicacid calibrator using a first set of amplification oligonucleotides, andamplifying the analyte polynucleotide standard using a second set ofamplification oligonucleotides, where the first and second sets ofamplification oligonucleotides are different from each other. Understill another alternative, the step for determining indicia ofamplification involves determining threshold-based indicia ofamplification. Under yet another alternative, the step for determiningindicia of amplification does not involve determining threshold-basedindicia of amplification. Under still yet another alternative, each ofthe first and second fitted equations has four coefficients. Underanother alternative, the in vitro nucleic acid amplification reaction inthe coamplifying step is an isothermal in vitro nucleic acidamplification reaction. Under another alternative, the isothermal invitro nucleic acid amplification reaction is a transcription-associatedamplification reaction.

Another aspect of the invention relates to a method of quantifying ananalyte nucleic acid contained in a test sample by internal calibrationadjustment of nucleic acid amplification results. The method includes afirst step for collecting a standard data set and a test data set. Thestandard data set includes results from a plurality of standard nucleicacid amplification reactions, where each standard nucleic acidamplification reaction includes a constant starting quantity of anucleic acid calibrator and a different known starting quantity of ananalyte polynucleotide standard. The plurality of standard nucleic acidamplification reactions yield indicia of amplification for the analytepolynucleotide standard as a function of the known starting quantity ofthe analyte polynucleotide standard, and indicia of amplification forthe nucleic acid calibrator that coamplified with the analytepolynucleotide standard as a function of the known starting quantity ofthe analyte polynucleotide standard. The test data set includes resultsfrom a test nucleic acid amplification reaction that includes theconstant starting quantity of the nucleic acid calibrator and an unknownstarting quantity of the analyte nucleic acid. The test nucleic acidamplification reaction yields an indicium of amplification for theanalyte nucleic acid contained in the test sample, and an indicium ofamplification for the nucleic acid calibrator that coamplified with theanalyte nucleic acid. Next, there is a step for preparing athree-dimensional parametric calibration curve that includes: (a) afirst dimension that includes solutions to a first optimized parametricequation that expresses indicia of amplification for the analytepolynucleotide standard as a function of the known starting quantity ofthe analyte polynucleotide standard; (b) a second dimension thatincludes solutions to a second optimized parametric equation thatexpresses indicia of amplification for the nucleic acid calibrator as afunction of the known starting quantity of analyte polynucleotidestandard; and (c) a third dimension parameter of the first and secondoptimized parametric equations. This third dimension parameter is afunction of the known starting quantity of analyte polynucleotidestandard used in the plurality of standard nucleic acid amplificationreactions. Notably, the first and second dimensions of thethree-dimensional parametric calibration curve define a measurementplane. This measurement plane includes a projection of thethree-dimensional parametric calibration curve. Next, there is a stepfor specifying a test sample data point in the measurement plane,wherein the test sample data point includes a set of coordinates for theindicium of amplification for the analyte nucleic acid and the indiciumof amplification for the nucleic acid calibrator that coamplified withthe analyte nucleic acid in the test nucleic acid amplificationreaction. Finally, there is a step for determining the minimum distancebetween the test sample data point specified in the measurement planeand the projection of the three-dimensional parametric calibration curvein the measurement plane by varying the value of the third dimensionparameter. The value of the third dimension parameter which results inthe determined minimum distance estimates the quantity of the analytenucleic acid contained in the test sample. In accordance with a firstgenerally preferred embodiment, the determining step involvesdetermining by an iterative computing process. When this is the case, itis desirable for the iterative computing process to involve calculatingthe hypotenuse length for a plurality of right triangles. Morepreferably, the plurality of standard nucleic acid amplificationreactions and the test nucleic acid amplification reaction areisothermal amplification reactions that do not use thermal cycling tosynthesize amplicons. In an alternative preferred embodiment, theplurality of standard nucleic acid amplification reactions and the testnucleic acid amplification reaction amplify the analyte nucleic acid andanalyte polynucleotide standard using a first set of two amplificationoligonucleotides, and amplify the nucleic acid calibrator using a secondset of two amplification oligonucleotides. In this instance, the firstand second sets of amplification oligonucleotides are identical to eachother. In another alternative preferred embodiment, the plurality ofstandard nucleic acid amplification reactions and the test nucleic acidamplification reaction amplify the analyte nucleic acid and analytepolynucleotide standard using a first set of two amplificationoligonucleotides, and amplify the nucleic acid calibrator using a secondset of two amplification oligonucleotides. In this instance, the firstand second sets of amplification oligonucleotides are not identical toeach other. In still another alternative preferred embodiment, thecollecting step, the preparing step, the specifying step, and thedetermining step are each automated by computer software that is anintegral component of a device used for performing the test nucleic acidamplification reaction and the plurality of standard nucleic acidamplification reactions. In accordance with another generally preferredembodiment, each of the plurality of standard nucleic acid amplificationreactions and the test nucleic acid amplification reaction can beisothermal amplification reactions that do not use thermal cycling tosynthesize amplicons. In accordance with another generally preferredembodiment, the plurality of standard nucleic acid amplificationreactions and the test nucleic acid amplification reaction can amplifythe analyte nucleic acid and analyte polynucleotide standard using afirst set of two amplification oligonucleotides, and amplify the nucleicacid calibrator using a second set of two amplificationoligonucleotides. In this instance the first and second sets ofamplification oligonucleotides are identical to each other. Inaccordance with another generally preferred embodiment, the plurality ofstandard nucleic acid amplification reactions and the test nucleic acidamplification reaction amplify the analyte nucleic acid and analytepolynucleotide standard using a first set of two amplificationoligonucleotides, and amplify the nucleic acid calibrator using a secondset of two amplification oligonucleotides. In this instance the firstand second sets of amplification oligonucleotides are not identical toeach other. In accordance with yet another generally preferredembodiment, the first and second optimized parametric equations eachhave four fixed coefficients.

Another aspect of the invention relates to a system for quantifying aninitial amount of an analyte polynucleotide contained in a test sample.Generally speaking, this system includes as key components: (1) anobtaining means, (2) a programmable processing means, and (3) areporting means. With specific reference to the first of thesecomponents, there is a means for obtaining (a) a standard data set oftime-dependent indicia of amplification for each of an analytepolynucleotide standard and a nucleic acid calibrator that coamplifiedtherewith in a plurality of in vitro nucleic acid standard amplificationreactions carried out using a range of starting amounts of analytepolynucleotide standard and a constant starting amount of nucleic acidcalibrator, and (b) a test data set of time-dependent indicia ofamplification for each of the analyte polynucleotide contained in thetest sample and a nucleic acid calibrator that coamplified therewith inan in vitro nucleic acid test amplification reaction. With specificreference to the second component of the system invention, there is aprogrammable means for processing the standard data set and the testdata set by comparing the test data set with a three-dimensionalcalibration curve prepared from the standard data set. Thethree-dimensional calibration curve includes a first dimension thatincludes solutions to a first optimized parametric equation thatexpresses indicia of amplification for analyte polynucleotide standardas a function of the known starting quantities of analyte polynucleotidestandard input into the in vitro nucleic acid standard amplificationreactions. The three-dimensional calibration curve further includes asecond dimension that includes solutions to a second optimizedparametric equation that expresses indicia of amplification forcoamplified nucleic acid calibrator as a function of the known startingquantities of analyte polynucleotide standard input into the in vitronucleic acid standard amplification reactions. The three-dimensionalcalibration curve further includes a third dimension parameter of thefirst and second optimized parametric equations. This third dimensionparameter includes the known starting quantities of analytepolynucleotide standard input into the in vitro nucleic acid standardamplification reactions. Notably, the first and second dimensions of thethree-dimensional parametric calibration curve define a measurementplane, and this measurement plane includes a projection of thethree-dimensional parametric calibration curve. With specific referenceto the third component of the invented system, there is a means forreporting a result obtained from the processed test data set thatquantifies the initial amount of analyte polynucleotide contained in thetest sample.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graphic presentation of an exemplary real-time run curveshowing the positions corresponding to different indicia ofamplification. Symbols on the run curve identify indicia ofamplification for TArc (□), OTArc (Δ), TTime (x), the maximum of thefirst derivative (⋄), and the maximum of the second derivative (◯).Notably, the determined OTArc and TTime indicia of amplification arenearly coincident.

FIG. 2 is graphic illustration of a procedure used for determining aTTime value. The x-axis displays the time interval, and the y-axisdisplays background-subtracted and normalized RFU (relative fluorescenceunits). A thin horizontal line indicates a fluorescence threshold.Fluorescence readings as a function of time are indicated by filleddiamonds (♦). The heavy line has been drawn to indicate the slope of thedata over the interval 0.04-0.36.

FIGS. 3A-3B graphically illustrate methods of determining TArc valuesusing directionally similar vectors (panel A), and methods ofdetermining OTArc values using directionally opposed vectors (panel B).Both panels show paired sets of two vectors (vectors “a” and “b”) drawnon a portion of a growth curve. The angle between the two vectors isidentified as ω.

FIG. 4 is a two-dimensional graph showing indicia of amplification(y-axis) plotted against the amount of analyte polynucleotide standard(x-axis) input into a reaction mixture for real-time amplificationreactions initiated with a constant quantity of nucleic acid calibrator.Data points showing results for known amounts of the analytepolynucleotide standard are depicted by open triangles (Δ), and datapoints showing results for the internal calibrator are depicted by opencircles (◯). Notably, some data points shown on the graph areoverlapping. Curves drawn on the graph are the result of curve fittingparametric equations.

FIG. 5 is a three-dimensional graph illustrating the relationshipbetween the indicia of amplification for the analyte polynucleotidestandard (Tt(S)) expressed in TTime units (i.e., minutes); the indiciaof amplification for the internal calibrator (ICt(S)) expressed in TTimeunits (i.e., minutes), and a function of the amount of analytepolynucleotide standard input into an amplification reaction, expressedas Z(S)=log₁₀(S). Data points representing determinations of the indiciaof amplification for individual amplification reactions are indicated byplus signs (+). The dashed heavy curve represents the three-dimensionalparametric calibration curve. The solid curve represents the parametriccalibration curve plotted in the measurement plane. The curve in themeasurement plane is the projection of the three-dimensional curve ontothe measurement plane.

FIGS. 6A-6B are graphs illustrating a parametric calibration curve and atest sample data point plotted in the measurement plane. FIG. 6A shows aparametric calibration curve and a test sample data point havingcoordinates (Tt?,ICt?). FIG. 6B shows how the distance between the testsample data point and different points on the two-dimensionalcalibration curve in the measurement plane can be calculated. Twoarbitrary points on the calibration curve are identified by(Tt(S)₁,ICt(S)₁) and (Tt(S)₂,ICt(S)₂). The distance separating the testsample data point and the calibration curve can be determined bycalculating the hypotenuse (δ) of a right triangle.

DEFINITIONS

The following terms have the following meanings for the purpose of thisdisclosure, unless expressly stated to the contrary herein.

As used herein, “polynucleotide” means either RNA, DNA, or a chimericmolecule containing both RNA and DNA.

By “analyte polynucleotide” or “analyte nucleic acid” is meant apolynucleotide of interest that is to be quantified.

As used herein, a “test sample” is any sample to be investigated for thepresence of a particular polynucleotide species. Test samples includeany tissue or polynucleotide-containing material obtained from a human,animal, environmental, or laboratory-derived or synthetic sample.

As used herein, “standard samples” are samples containing an analytepolynucleotide standard.

By “analyte polynucleotide standard” is meant a known quantity of ananalyte polynucleotide, or fragment thereof. For example, an HIV-1analyte polynucleotide standard may contain a known number of copies ofan HIV-1 genome, HIV-1 transcript, or in vitro synthesized transcriptrepresenting a portion of the viral genome.

An “amplicon” is a polynucleotide product of an amplification reactionwherein a target nucleic acid sequence served as the template forsynthesis of polynucleotide copies or amplification products.

By “amplification” or “nucleic acid amplification” or “in vitro nucleicacid amplification” is meant any known procedure for obtaining multiplecopies, allowing for RNA and DNA equivalents, of a target nucleic acidsequence or its complement or fragments thereof. Amplification of“fragments thereof” refers to production of an amplified nucleic acidcontaining less than the complete target region nucleic acid sequence orits complement. Such fragments may be produced by amplifying a portionof the target nucleic acid, for example, by using an amplificationoligonucleotide which hybridizes to, and initiates polymerization from,an internal position of the target nucleic acid.

As used herein, “thermal cycling” refers to repeated changes oftemperature, (i.e., increases or decreases of temperature) in a reactionmixture. Samples undergoing thermal cycling may shift from onetemperature to another, stabilize at that temperature, transition to asecond temperature or return to the starting temperature. Thetemperature cycle may be repeated as many times as required to study orcomplete the particular chemical reaction of interest.

By “target nucleic acid” or “target” is meant a nucleic acid containinga target nucleic acid sequence. In general, a target nucleic acidsequence that is to be amplified will be positioned between twooppositely disposed oligonucleotides, and will include the portion ofthe target nucleic acid that is complementary to each of theoligonucleotides.

By “target nucleic acid sequence” or “target sequence” or “targetregion” is meant a specific deoxyribonucleotide or ribonucleotidesequence comprising all or part of the nucleotide sequence of asingle-stranded nucleic acid molecule, and the deoxyribonucleotide orribonucleotide sequence complementary thereto.

By “transcription-associated amplification” is meant any type of nucleicacid amplification that uses an RNA polymerase to produce multiple RNAtranscripts from a nucleic acid template. Conventionally, theseamplification reactions employ at least one primer having a 3′-end thatcan be extended by the activity of a DNA polymerase. One example of atranscription-associated amplification method, called “TranscriptionMediated Amplification” (TMA), generally employs an RNA polymerase, aDNA polymerase, deoxyribonucleoside triphosphates, ribonucleosidetriphosphates, and a promoter-containing oligonucleotide complementaryto the target nucleic acid. Variations of TMA are well known in the artas disclosed in detail in Burg et al., U.S. Pat. No. 5,437,990; Kacianet al., U.S. Pat. Nos. 5,399,491 and 5,554,516; Kacian et al., PCT No.WO 93/22461; Gingeras et al., PCT No. WO 88/01302; Gingeras et al., PCTNo. WO 88/10315; Malek et al., U.S. Pat. No. 5,130,238; Urdea et al.,U.S. Pat. Nos. 4,868,105 and 5,124,246; McDonough et al., PCT No. WO94/03472; and Ryder et al., PCT No. WO 95/03430. Othertranscription-associated amplification methods employing only a singleprimer that can be extended by a DNA polymerase, as disclosed in theU.S. patent application having Ser. No. 11/213,519 are particularlyembraced by the definition and are highly preferred for use inconnection with the method disclosed herein.

As used herein, an “oligonucleotide” or “oligomer” is a polymeric chainof at least two, generally between about five and about 100, chemicalsubunits, each subunit comprising a nucleotide base moiety, a sugarmoiety, and a linking moiety that joins the subunits in a linear spacialconfiguration. Common nucleotide base moieties are guanine (G), adenine(A), cytosine (C), thymine (T) and uracil (U), although other rare ormodified nucleotide bases able to hydrogen bond are well known to thoseskilled in the art. Oligonucleotides may optionally include analogs ofany of the sugar moieties, the base moieties, and the backboneconstituents. Preferred oligonucleotides of the present invention fallin a size range of about 10 to about 100 residues. Oligonucleotides maybe purified from naturally occurring sources, but preferably aresynthesized using any of a variety of well known enzymatic or chemicalmethods.

By “amplification oligonucleotide” or “amplification oligomer” is meantan oligomer that hybridizes to a target nucleic acid, or its complement,and participates in a nucleic acid amplification reaction. Examples ofamplification oligomers include primers that contain a 3′ end that isextended as part of the amplification process, but also includeoligomers that are not extended by a polymerase (e.g., a 3′ blockedoligomer) but may participate in, or facilitate efficient amplificationfrom a primer. Preferred size ranges for amplification oligomers includethose that are about 10 to about 60 nt long and contain at least about10 contiguous bases, and more preferably at least 12 contiguous basesthat are complementary to a region of the target nucleic acid sequence(or a complementary strand thereof). The contiguous bases are preferablyat least about 80%, more preferably at least about 90%, and mostpreferably about 100% complementary to the target sequence to whichamplification oligomer binds. An amplification oligomer may optionallyinclude modified nucleotides or analogs, or additional nucleotides thatparticipate in an amplification reaction but are not complementary to orcontained in the target nucleic acid. An amplification oligomer that is3′ blocked but capable of hybridizing to a target nucleic acid andproviding an upstream promoter sequence that serves to initiatetranscription is referred to as a “promoter provider” oligomer.

A “primer” is an amplification oligomer that hybridizes to a templatenucleic acid and has a 3′ OH end that can be extended by a DNApolymerase. The 5′ region of the primer may be non-complementary to thetarget nucleic acid (e.g., a promoter sequence), resulting in anoligomer referred to as a “promoter-primer.” Those skilled in the artwill appreciate that any oligomer that can function as a primer can bemodified to include a 5′ promoter sequence, and thus could function as apromoter-primer. Similarly, any promoter-primer can be modified byremoval of, or synthesis without, a promoter sequence and still functionas a primer.

As used herein, a “set” of amplification oligonucleotides refers to acollection of two or more amplification oligonucleotides thatcooperatively participate in an in vitro nucleic acid amplificationreaction to synthesize amplicons.

As used herein, a “probe” is an oligonucleotide that hybridizesspecifically to a target sequence in a nucleic acid, preferably in anamplified nucleic acid, under conditions that promote hybridization, toform a detectable hybrid.

As used herein, “time-dependent” monitoring of nucleic acidamplification, or monitoring of nucleic acid amplification in“real-time” refers to a process wherein the amount of amplicon presentin a nucleic acid amplification reaction is measured as a function ofreaction time or cycle number and then used to determine a startingamount of template that was present in the reaction mixture at the timethe amplification reaction was initiated. For example, the amount ofamplicon can be measured prior to commencing each complete cycle of anamplification reaction that comprises thermal cycling, such as PCR.Alternatively, isothermal amplification reactions that do not requirephysical intervention to initiate the transitions between amplificationcycles can be monitored continuously, or at regular time intervals toobtain information regarding the amount of amplicon present as afunction of time.

As used herein, a “growth curve” refers to the characteristic pattern ofappearance of a synthetic product, such as an amplicon, in a reaction asa function of time or cycle number. A growth curve is convenientlyrepresented as a two-dimensional plot of time (x-axis) against someindicator of product amount, such as a fluorescence measurement(y-axis). Some, but not all, growth curves have a sigmoid-shape.

As used herein, the “baseline phase” of a growth curve refers to theinitial phase of the curve wherein the amount of product (such as anamplicon) increases at a substantially constant rate, this rate beingless than the rate of increase characteristic of the growth phase (whichmay have a log-linear profile) of the growth curve. The baseline phaseof a growth curve typically has a very shallow slope, frequentlyapproximating zero.

As used herein, the “growth phase” of a growth curve refers to theportion of the curve wherein the measurable product substantiallyincreases with time. Transition from the baseline phase into the growthphase in a typical nucleic acid amplification reaction is characterizedby the appearance of amplicon at a rate that increases with time.Transition from the growth phase to the plateau phase of the growthcurve begins at an inflection point where the rate of ampliconappearance begins to decrease.

As used herein, the “plateau phase” of a triphasic growth curve refersto the final phase of the curve. In the plateau phase, the rate ofmeasurable product formation generally is substantially lower than therate of amplicon production in the log-linear phase, and may evenapproach zero.

As used herein, the phrase “indicia of amplification” refers to featuresof real-time run curves which indicate a predetermined level of progressin nucleic acid amplification reactions. Such indicia are commonlydetermined by mathematical analysis of run curves, sometimes referred toas “growth curves,” which display a measurable signal (such as afluorescence reading) whose intensity is related to the quantity of anamplicon present in a reaction mixture as a function of time, cyclenumber, etc.

By “nucleic acid calibrator” or “internal calibrator” is meant apolynucleotide that is capable of amplification in an in vitro nucleicacid amplification reaction, and that is distinguishable from an analytepolynucleotide coamplified in the same amplification reaction. Incertain preferred embodiments, the internal calibrator and the analytepolynucleotide are coamplified in an in vitro nucleic acid amplificationreaction using one or more different amplification oligomers or primers.For example, the analyte and internal calibrator polynucleotidesemployed in the working Examples detailed below were amplified usingamplification oligonucleotides that were not shared. In other preferredembodiments, the internal calibrator and the analyte polynucleotide arecoamplified in an in vitro nucleic acid amplification reaction usingidentical amplification oligomers or primers.

As used herein, “internal calibration adjustment” refers to aquantitative procedure for determining the starting amount of analytenucleic acid in a test sample that underwent amplification by comparisonwith results obtained for a coamplified target nucleic acid referred toas a “nucleic acid calibrator” or “internal calibrator.”

By “parametric equation” is meant an equation that allows variables,called “parameters” or independent variables, to be filled-in with anyspecified value to obtain the values of dependent variables. Forexample, if a two-dimensional curve is traced out as a function of athird variable S, then the position along the curve at any value of Scan be described by parametric equations: x=x(S) and y=y(S). Then x andy are related to each other through their dependence on the “parameter”S.

As used herein, a “parameter” is the independent variable in a set ofparametric equations.

As used herein, a “parametric calibration curve” is a mathematicalrelationship, including visual displays and electronic representationsthereof, between (a) indicia of amplification for known amounts ofanalyte polynucleotide standard as a function of the parameterrepresenting the known starting quantity of analyte polynucleotidestandard present in a reaction mixture at the time an amplificationreaction was initiated (i.e., “Tt(S)”), and (b) indicia of amplificationfor a known, constant amount of nucleic acid calibrator that coamplifiedwith the analyte polynucleotide standard in the same amplificationreaction as a function of the parameter representing the known startingquantity of analyte polynucleotide standard present in the reactionmixture at the time the amplification reaction was initiated (i.e.,“ICt(S)”). For example, a three-dimensional parametric calibration curvemay display, or relate in electronic spreadsheet format, Tt(S) in onedimension, ICt(S) in another dimension, and the known starting quantityof analyte polynucleotide standard present in a reaction mixture at thetime the amplification reaction was initiated (i.e., “S”) in a thirddimension. A projection of this three-dimensional calibration curve ontothe two-dimensional measurement plane represents a two-dimensionalparametric calibration curve.

As used herein, a “parametric calibration method” is a quantitativemethod involving the preparation and/or use of a parametric calibrationcurve.

As used herein, the phrase “as a function of” describes the relationshipbetween a dependent variable (i.e., a variable that depends on one ormore other variables) and an independent variable (i.e., a variable thatmay have its value freely chosen without considering the values of anyother variables), wherein each input value for the independent variablerelates to exactly one output value for the dependent variable.

As used herein, “optimizing” a parametric equation refers to a process,as commonly practiced in mathematical modeling or curve fittingprocedures, for obtaining numerical values for coefficients in aparametric equation to yield an expression that “fits” or approximatesexperimental measurements.

As used herein, the terms “optimized parametric equation,” and “fittedequation” and “fitted parametric equation” are alternative references toa parametric equation containing fixed numerical values for coefficientsas the result of an optimizing procedure.

As used herein, “incremental” values refer to values that increase ordecrease gradually by regular degrees.

As used herein, an “iterative” computing method attempts to solve aproblem (e.g., an equation or system of equations) by successiveapproximations to the solution.

As used herein, the phrase “threshold-based indicia of amplification”refers to indicia of amplification that require quantifying a baselinesignal for amplicon synthesis, and that further require a calculation(such as calculation of a difference or a quotient) based on thisquantified baseline signal. TTime determinations are examples ofthreshold-based indicia of amplification, while TArc and OTArcdeterminations are examples of non-threshold-based indicia ofamplification.

As used herein, “specifying” in a plane (e.g., specifying a data pointin a measurement plane) refers to a procedure, which may involve use ofcomputer software, for designating a point in the plane of atwo-dimensional graph. This can involve identifying coordinates (e.g., xand y coordinates) for the data point in the plane.

By “consisting essentially of” is meant that additional component(s),composition(s) or method step(s) that do not materially change the basicand novel characteristics of the present invention may be included inthe present invention. Any component(s), composition(s), or methodstep(s) that have a material effect on the basic and novelcharacteristics of the present invention would fall outside of thisterm.

DETAILED DESCRIPTION OF THE INVENTION

Herein there are disclosed methods for improving the quantitation ofanalyte polynucleotides using real-time nucleic acid amplification. Morespecifically, the invention relates to methods for assessing internalcalibration results in real-time amplification assays, and toadjustments in the quantitation of an analyte polynucleotide that takeinto account the internal calibration results, thereby improving assayprecision and accuracy. These methods allow for correction ofsample-to-sample variability where target amounts are identical, butamplification conditions differ slightly. Using a space curve parametriccalibration, measured indicia from the amplification profiles of both ananalyte polynucleotide and an internal calibrator are used to estimatethe analyte polynucleotide copy number present in an unknown testsample.

In accordance with certain embodiments of the disclosed method, resultsfrom real-time amplification reactions are processed to calculateindicia of amplification. Generally speaking, these indicia areindicators of the extent of an amplification reaction. The measured orcalculated indicia of amplification can then be used to generate twodifferent two-dimensional plots—one for an analyte polynucleotidestandard and another for an internal calibrator. More specifically, themeasured indicia of amplification for these targets are plotted againstsome measure of the number of copies of analyte polynucleotide standardinput into the amplification reaction. Information from these plots canthen be combined to create a calibration space curve, such as athree-dimensional calibration curve. The data sets used in theseprocedures are generated from a collection of amplification reactions,each containing a known number of copies of an analyte polynucleotidestandard, and each containing a constant number of internal calibratortemplates prior to initiating the amplification reaction.

The variables (i.e., “coefficients”) of a model parametric equation canbe fitted to the data points for each of the two-dimensional plots toresult in two equations that define curves fitting the measured values.More specifically, the coefficients of a preselected parametric equationcan be optimized or determined by fitting the model equation to themeasured data points. This can be accomplished by solving for numericalvalues of the coefficients that minimize differences between measureddata and model (i.e., fitted) values, thereby resulting in a fittedcurve. Those having an ordinary level of skill in the art will recognizethat these procedures can be carried out using curve-fitting techniques.One of the resulting equations expresses the measurable indicia ofamplification for known quantities of the analyte polynucleotidestandard (Tt) as a first function of the known number of analytepolynucleotide standard molecules (S) input into the reaction (i.e.,Tt=Tt(S)). The second equation expresses the measurable indicia ofamplification for the internal calibrator (ICt) as a second function ofthe known number of analyte polynucleotide standard molecules input intothe reaction (i.e., ICt=ICt(S)). In this manner Tt and ICt are relatedto each other through their dependence on the parameter S. A thirdequation expresses the number of analyte polynucleotide molecules inputinto the amplification reaction (Z) as a function of the known number ofanalyte polynucleotide standard molecules input into the reaction (i.e.,Z=Z(S)). For example, in certain specific embodiments this thirdfunction may take the form Z=log₁₀(S).

The calibration relationships can be plotted as a parametric curve inthe measurement plane with each data point having coordinates (Tt, ICt),where the number of analyte polynucleotide standard molecules (S) is theparameter of the curve in the measurement plane. Alternatively, thecalibration relationship can be plotted as a space-curve in threedimensions where the parameter S is plotted as the height above themeasurement plane. The indicia of amplification for the analytepolynucleotide and internal calibrator amplified in a test reactioncontaining an unknown number of analyte polynucleotide molecules canalso be plotted in the measurement plane of the parametric calibrationplot.

FIG. 6A illustrates a two-dimensional relationship corresponding to theprojection onto the measurement plane of a three-dimensional parametriccalibration curve, such as that shown in FIG. 5. Also shown is a testsample data point, indicated by (Tt?,ICt?), representing the indicia ofamplification coordinates for analyte and internal calibratorpolynucleotides in an amplification reaction initiated with an unknownnumber of analyte polynucleotide molecules. This test sampleamplification reaction also included the same constant amount ofinternal calibrator employed in all of the standard reactions used forcreating the calibration curves. As discussed above, there are at leasttwo methods for producing the two-dimensional relationship shown in thefigure. Of course, since Z=Z(S), the z-axis is assumed in the graphspresented in FIGS. 6A-6B. Thus, FIG. 6A illustrates specification in themeasurement plane of a parametric calibration curve relating thecoordinates of the indicia of amplification measured for the coamplifiedanalyte polynucleotide and internal calibrator in a test reaction.

To estimate the starting analyte polynucleotide copy number used in thetest reaction, the value of S on the parametric calibration curve in themeasurement plane is varied to locate the point on the calibration curvein the measurement plane that is nearest to the test sample coordinatesin the measurement space. The distance between the coordinate for thetest sample in the measurement space and a point on the modelcalibration space curve can be calculated simply by using the Euclideannorm and the following equation.δ²=(Tt?−Tt(S))²+(ICt?−ICt(S))²  (Eq 1)In this equation, the square of the hypotenuse (δ) of a right trianglewhich defines the distance between the test coordinate in themeasurement plane (Tt?, ICt?) and a point on the calibration curve inthe measurement plane determined for a particular S value (Tt(S),ICt(S)) equals the square of the difference between the measured indiciaof amplification for the unknown analyte polynucleotide and the indiciaof amplification for a point on the calibration curve (i.e.,(Tt?−Tt(S))²) added to the square of the difference between the measuredindicia of amplification for the internal calibrator in the testreaction and the indicia of amplification for a point on the calibrationcurve (i.e., (ICt?−ICt(S))²). The analyte polynucleotide copy numbervalue (i.e., the value of S in the z-dimension) on the parametriccalibration curve corresponding to that value of S which gives theminimal distance (i.e., minimal δ) between the test sample coordinate inthe measurement plane and the calibration curve estimates the analytepolynucleotide copy number in the test sample. Those having an ordinarylevel of skill in the art will appreciate that determination of thevalue of S that provides this minimal distance can be accomplished usinga reiterative computing process that involves calculating the value of δat different values of S.

FIG. 6B particularly illustrates this method of estimating the amount ofanalyte polynucleotide in a test sample that would give rise to the datapoint having the coordinates (Tt?,ICt?), as shown in FIG. 6A. The methodpreferably involves varying the value of the parameter S to locate thepoint on the parametric calibration curve in the measurement plane whichis nearest to the test sample data point in the measurement plane.Determining the value of S that minimizes the magnitude of theseparation between the data point having the coordinates (Tt?,ICt?) andthe parametric calibration curve projection in the measurement planeestimates the amount of analyte polynucleotide contained in the testsample. The magnitude of the separation between the parametriccalibration curve in the measurement plane and the point representingthe coordinates for the test sample is indicated by the symbol, “δ.”FIG. 6B shows two arbitrary points on the parametric calibration curvein relation to the test sample data point. Each point is associated witha unique set of coordinates (Tt(S),ICt(S)). Coordinates for the testsample data point are (Tt?,ICt?). Each of the points identified on thecalibration curve in the measurement plane can be used to generate atriangle that is unique for each level of input analyte polynucleotide.In each case the hypotenuse of the triangle represents the magnitude ofseparation between the test data point and the curve drawn in themeasurement plane. The magnitude of the hypotenuse can be calculatedsimply by applying the Pythagorean theorem, as embodied in Equation (1).

Notably, the present method for analyzing and using results from acoamplifiable internal calibrator differs substantially from previouslydescribed methods. For example, the disclosed method applies equallywell to data obtained when the analyte polynucleotide and internalcalibrator nucleic acids amplify using the same amplificationoligonucleotides, or different amplification oligonucleotides. Also,there is no requirement for establishing ratios between measured valuesdetermined for standards and internal calibrators. Moreover, thedisclosed method generalizes to any form of calibration fittingfunctions, and it generalizes to larger numbers of independentmeasurements. For example, if each of the time records of analytepolynucleotide standard and internal calibrator are characterized by twoindicia each, the four indicia would form a four-dimensional hyperplaneand the calibration curve would be a five-dimensional space curve. Thus,the method disclosed herein is broadly applicable, and its value is notlimited to a particular in vitro amplification method.

Useful Amplification Methods

Examples of amplification methods useful in connection with theparametric calibration method include, but are not limited to:Transcription Mediated Amplification (TMA), Single-Primer Nucleic AcidAmplification, Nucleic Acid Sequence-Based Amplification (NASBA), thePolymerase Chain Reaction (PCR), Strand Displacement Amplification(SDA), Self-Sustained Sequence Replication (3SR), DNA Ligase ChainReaction (LCR) and amplification methods using self-replicatingpolynucleotide molecules and replication enzymes such as MDV-1 RNA andQ-beta enzyme. Methods for carrying out these various amplificationtechniques respectively can be found in U.S. Pat. No. 5,399,491,published U.S. patent application Ser. No. 11/213,519, publishedEuropean patent application EP 0 525 882, U.S. Pat. No. 4,965,188, U.S.Pat. No. 5,455,166, Guatelli et al., Proc. Natl. Acad. Sci. USA87:1874-1878 (1990), International Publication No. WO 89/09835, U.S.Pat. No. 5,472,840 and Lizardi et al., Trends Biotechnol. 9:53-58(1991). The disclosures of these documents which describe how to performnucleic acid amplification reactions are hereby incorporated byreference.

Amplification reactions that require only a single extendable primer areparticularly preferred for use in connection with the disclosedcalibration method. These reactions include transcription-associatedamplification systems that employ a single extendable primer incombination with a 3′-blocked oligonucleotide that cannot be extended bya nucleic acid polymerase. Methods for carrying out such amplificationreactions are, for example, detailed in U.S. patent application Ser. No.11/213,519.

Examples of Useful Indicia of Amplification

A variety of indicia of amplification can be used in connection with thedisclosed method. For example, mathematical and computing techniquesthat will be familiar to those having an ordinary level of skill in theart can be used to identify the time of occurrence of the maximum of thefirst derivative, or the time of occurrence of the maximum of the secondderivative of a real-time run curve. Approaches for determining thesefeatures of a growth curve have been detailed by Wittwer et al., in U.S.Pat. No. 6,503,720, the disclosure of which is incorporated by referenceherein. Other useful approaches involve calculating a derivative of agrowth curve, identifying a characteristic of the growth curve, and thendetermining the threshold time or cycle number corresponding to thecharacteristic of the derivative. Such techniques have been disclosed inU.S. Pat. No. 6,783,934, the disclosure of which is incorporated byreference. Still other useful indicia of amplification include “TTime,”“TArc” and “OTArc.”

FIG. 1 shows that the above-referenced indicia of amplification identifydifferent points on the same real-time run curve. Nevertheless, each ofthese different indicia can be used in accordance with the disclosedcalibration algorithm to create a calibration curve or plot. Thisillustrates the versatility of the technique described herein.

Methods of Determining TTime Values

Simply stated, TTime values estimate the time at which a particularthreshold indicating amplicon production is passed in a real-timeamplification reaction. The algorithm for calculating and using TTimevalues has been described in U.S. patent application Ser. No.60/659,874, the disclosure of which is incorporated by reference. FIG. 2illustrates the method of determining a TTime value on a segment of areal-time run curve.

To illustrate the general features of the TTime determination, it willbe assumed that data collected as a series of time-based fluorescencereadings was obtained, and that such data can be referred to in terms ofRelative Fluorescent Units (“RFUs”). Each data point, measured at agiven time interval, is referred to as RFU(t). In general, each RFU(t)plot is characterized by an initial, substantially flat portion at ornear a minimum level, followed by an abrupt and relatively steeplysloped portion, and ending with a generally flat portion at or near amaximum level.

The TTime (also known as “time-of-emergence”) refers to the time atwhich the data RFU(t), normalized as discussed below, reaches apredefined threshold value. Using standard curves, as will be describedin more detail below, the TTime determined for a particular sample can,without adjustment for amplification of an internal calibrator, becorrelated with an analyte amount or concentration, thereby indicatingthe analyte amount or concentration for the sample. In general, thehigher the concentration of the analyte of interest, the steeper theRFU(t) curve and the sooner the TTime.

The first step of the TTime determination procedure is backgroundadjustment and normalization of the data. Background adjustment isperformed to subtract that portion of the signal data RFU(t) that is dueto background “noise” from, for example, stray electromagnetic signalsfrom other modules in the instrument used for conducting and monitoringnucleic acid amplification reactions. Background adjustment is performedby simply subtracting a background value “BG” from the data RFU(t) toobtain adjusted data RFU*(t). That is, RFU*(t)=RFU(t)−BG.

The background BG, is determined as follows. First, determine the timeintervals between data points. The time interval is determined bymultiplying cycle time (i.e., the time between consecutive datameasurements) by the data point (i.e., 0th data point, 1st data point,2nd data point, . . . nth data point) and divide by 60 seconds. Forexample, assuming a cycle time of 30 seconds, the time interval for the15th data point is (15×30 sec.)/60 sec.=7.5 minutes. Next, find themidpoint of the signal data by adding the minimum signal data point andthe maximum signal data point and dividing by two. That is:(RFU_(max)+RFU_(min))/2. Starting at the time corresponding to themidpoint value and working backwards, calculate the slope for each pairof data points:

(RFU(t)−RFU(t−1))/Δt(t→t−1). Find where the slope of RFU(t) flattens outby finding the first slope value that is less than the static slopevalue (i.e., the value before the RFU(t) curve begins its upward slope,e.g., −0.0001). Once this slope is found, find the next slope that isnot negative; this value is H_(index). Next, take the mean of the entirerange of RFU(t) values starting at the first data point and go to theRFU value that corresponds to the H_(index) value. Preferably, the meanof this data is taken using the TRIMMEAN function of an EXCELspreadsheet (Microsoft Corporation; Redmond, Wash.) on this range ofdata using a static back trim value of 0.15. This mean value is thebackground, BG.

To normalize the data, each data point, adjusted for the background, isdivided by the maximum data point, also adjusted for the background.This can be calculated as follows.

$\begin{matrix}{{{Normalized}\mspace{14mu}{RFU}} = {{{RFU}_{n}(t)} = {\frac{{RFU}^{*}(t)}{{RFU}_{\max}^{*}} = \frac{{{RFU}(t)} - {BG}}{{RFU}_{\max} - {BG}}}}} & \left( {{Eq}\mspace{14mu} 2} \right)\end{matrix}$Thus, the RFU_(n)(t) will be between 0 and 1.

Next, the range of data is calculated by subtracting RFU_(n(min)) fromRFU_(n(max)). If the calculated range does not meet or exceed aspecified, minimum range (e.g., 0.05), the data is considered suspectand of questionable reliability, and, thus, the TTime will not becalculated. The minimum range is determined empirically and may varyfrom one fluorescence measuring instrument to the next. Ideally, thespecified minimum range is selected to ensure that the variation of datavalues from minimum to maximum exceeds the noise of the system.

Next, a curve fit procedure is applied to the normalized,background-adjusted data. Although any of the well-known curve fitmethodologies may be employed, in a preferred embodiment, a linear leastsquares (“LLS”) curve fit is employed. The curve fit is performed foronly a portion of the data between a predetermined low bound and highbound. The ultimate goal, after finding the curve which fits the data,is to find the time corresponding to the point at which the curveintersects a predefined threshold value. In the preferred embodiment,the threshold for normalized data is 0.11. The high and low bounds aredetermined empirically as that range over which curves fit to a varietyof control data sets exhibit the least variability in the timeassociated with the given threshold value. In the preferred embodiment,the low bound is 0.04 and the high bound is 0.36. The curve is fit fordata extending from the first data point below the low bound through thefirst data point past the high bound.

Next, determine whether the slope of the fit is statisticallysignificant. For example, if the p value of the first order coefficientis less than 0.05, the fit is considered significant, and processingcontinues. If not, processing stops. Alternatively, the validity of thedata can be determined by the R² value.

The slope (m) and intercept (b) of the linear curve are determined forthe fitted curve. With that information, TTime can be determined by thefollowing equation.

$\begin{matrix}{{TTime} = \frac{{Threshold} - b}{m}} & \left( {{Eq}\mspace{14mu} 3} \right)\end{matrix}$

Methods of Determining TArc Values

Time-dependent indicia of amplification referred to as “TArc” and“OTArc” are determined using vector-based analyses of real-time runcurves. The TArc value identifies the point in time at which a growthcurve begins to curve or “inflect” upward. This determined point can beused for creating a standard curve, or for establishing a parameter ofan amplification reaction that relates to the amount or concentration ofan analyte polynucleotide in a test sample. The vector analysis is mostconveniently carried out using growth curves having data pointsdistributed over substantially uniform time intervals. Detailedpresentations concerning the determination and use of TArc and OTArcvalues appear in U.S. patent application Ser. No. 11/474,698, thedisclosure contained in the specification and drawings of thisapplication being incorporated by reference herein. The essentialconcepts underlying the vector analysis are simply illustrated in FIGS.3A-3B.

Determining TArc Values Using Directionally Similar Vectors

One approach for determining a TArc value employs paired sets of vectorsthat are directionally similar. This means that the vectors share thesame direction in their x-components. Thus, vectors that aredirectionally similar will have x-components directed toward increasingx-values. This is distinguished from the situation characterizingdirectionally opposed vectors, wherein one vector is directed oppositethe other in the x-component.

FIG. 3A illustrates the arrangement of paired sets of directionallysimilar vectors drawn on a portion of an example growth curve. Asindicated in the figure, a first vector (i.e., vector a) is establishedhaving its tail positioned on a first data point (x1,y1) of the growthcurve, and its head positioned on a second data point (x2,y2) of thesame growth curve. The x-component (i.e., the time or cycle number axis)of the second data point has a value greater than the x-component of thefirst data point (i.e., x2>x1). For the purpose of illustration, if thegrowth curve is parsed into 5 second intervals in the time dimension,then the time value of the first data point can be 0 seconds and thetime value of the second data point can be 5 seconds. In thisillustration the time values of the two data points would be spacedapart by one unit (i.e., 5 seconds) in the time dimension of the growthcurve. The magnitude of the first vector would simply be the distanceseparating the first and second data points. The y-components of thefirst and second data points correspond to the magnitudes of theamplicon signals measured at the specified time points. A second vector(vector b) is established having its tail positioned on the same firstdata point (x1,y1) of the growth curve that was used for the firstvector, and its head positioned on a third data point (x3,y3) of thegrowth curve having an x-component greater than the x-component of thesecond data point of the first vector (i.e., x3>x2). For example, if thetime dimension values of the two data points used to establish the firstvector are separated by one unit on the x-axis, then the two data pointsused to establish the second vector should be separated on the x-axis byan amount greater than this number. Indeed, the magnitude of thex-component of the second vector can be greater than the magnitude ofthe x-component of the first vector by at least 2 fold, and can be ashigh as 20 fold, or more.

In accordance with the method of determining TArc using directionallysimilar vectors, paired sets of two vectors (i.e., vector a and vectorb), are established at regular time intervals, or cycle numberintervals, along the growth curve, with each vector of a single set ofpaired vectors sharing a common origin (i.e., the data pointcorresponding to the tail of each vector). The x-components of the firstand second vectors are spaced apart by predetermined values that areheld constant for the analysis. For example, if the magnitude of thex-component of the first vector in each pair is 5 seconds, then themagnitude of the x-component of the second vector in each pair can beheld constant at, for example, 85 seconds. This results in a pluralityof paired sets of two vectors, with the origins of the different pairedsets of vectors being positioned at different time points. Next, theorigins of paired sets of directionally similar vectors are incrementedalong the time axis (i.e., the x-axis) in a reiterative process ofestablishing paired sets of vectors. Preferably, a plurality of theregularly spaced time points along the growth curve serve as the originsof different paired set of vectors.

Once the paired sets of vectors are established, at least one featurecharacterizing the relationship between two vectors of a single set isthen determined. For example, the angle (ω) between the two vectors canbe determined using standard mathematical techniques that will befamiliar to those having an ordinary level of skill in the art. Thedetermined angle is associated with a time, or cycle number value alongthe growth curve. For example, the angle between two vectors (i.e.,vector a and vector b) can be determined according to Equation (4).ω=arccos [a·b/(∥a∥∥b∥)]  (Eq 4)Those having an ordinary level of skill in the art will understand fromEquation (4) that the dot product of two vectors has the propertydefined by Equation (5), where angle omega (6)) is the angle betweenvector a and vector b (assuming that the two vectors are non-zero, sothe angle between them is well defined). The angle between the vectorshas a numerical value in the interval (0, π). Since the dot product andthe norms of the vectors are easily computed, one can use this formulato calculate the angle between the vectors.a·b=∥a∥∥b∥cos(ω)  (Eq 5)Each time value along the x-axis of the growth curve is associated withan angle value. This conveniently can be accomplished using a tabularformat.

As illustrated in FIG. 3A, the angle (ω) between the two directionallysimilar vectors reaches a maximum value within the time intervalencompassing the upward concave inflection of the growth curve, and thatpoint on the time axis is said to be the “TArc.” Because the two vectorswill be separated by substantial angles at the initiation and conclusionof the growth phase or log-linear phase of the growth curve, and becausethe time values corresponding to the first instance are of greatestinterest, it is convenient, but not required to perform the vectoranalysis on the portion of the growth curve that precedes the conclusionof the growth phase of the growth curve. This can be accomplished, forexample by using a sliding window vector analysis that excludes theportion of the curve characterized by convex curvature and the plateauphase. Determining the point at which ω is maximal over the analyzedportion of the growth curve can be accomplished simply by sorting acolumn of numbers, as will be familiar to those acquainted with commonlyused computer spreadsheet programs, and then identifying the time pointor cycle number associated with the maximum angle value in the column.It is unnecessary to calculate derivatives or slopes of curve portionsto determine the maximal TArc value.

The TArc values determined in this manner can then be used forquantitative analysis of polynucleotide amounts or concentrations. Moreparticularly, once the TArc values are established for amplificationreactions conducted using known amounts of target or calibrator, thosedata points can be saved, plotted on a graph, or otherwise employed toestablish a standard curve Likewise, the TArc value determined for anamplification reaction performed using an unknown starting amount ofanalyte polynucleotide can be compared with a standard curve todetermine the starting amount of analyte polynucleotide in a sampleundergoing testing.

Thus, the vector-based algorithm illustrated in FIG. 3A employed pairedsets of two vectors that were directionally similar in the x-dimension.This arrangement required the vectors to have different magnitudes inthe x-dimension to create the opportunity for an angle therebetween asthe two vectors incremented along the growth curve. The algorithmfurther involved identifying, as a feature of the curve, the point onthe x-axis at which the smaller angle between the two vectors becamemaximal. When derived from analysis of reactions conducted using knownquantities of an analyte polynucleotide standard, the numerical value ofthis feature could be plotted against the log₁₀ of the input target copynumber to create a standard curve. Alternatively, if the feature wasderived from analysis of a reaction conducted using a test sample, thedetermined feature could be compared with a standard plot to determinethe starting amount or concentration of analyte polynucleotide presentin the test sample.

Determining OTArc Values Using Directionally Opposed Vectors

An alternative vector-based algorithm that can be used for determiningOTArc values similarly involves a reiterative process of establishingpaired sets of vectors along a growth curve, but employs directionallyopposed vectors instead of directionally similar vectors. In contrastwith the algorithm employing directionally similar vectors, thealgorithm employing directionally opposed vectors does not require bothof the vectors in the paired sets to have different magnitudes in thex-dimension, and involves identifying the point along the x-axis atwhich the angle between two vectors became minimal rather than maximal.In accordance with this latter approach, paired sets of two vectors canbe established such that they are directionally opposed in thex-dimension relative to the shared origin of the two vectors. Ingeneral, one member of a pair of directionally opposed vectors extendsfrom the shared origin in the direction of decreasing x-values, whilethe other member of the pair extends in the direction of increasingx-values.

Key aspects of the algorithm which employs directionally opposedvectors, and its relationship to the algorithm which employsdirectionally similar vectors, can be understood with reference to FIG.3B. This figure schematically illustrates how paired sets ofdirectionally opposed vectors can be incremented along the x-dimensionof a growth curve, and demonstrates how the angle between the twovectors becomes minimal in the vicinity of the transition between thebaseline and growth phases of the growth curve. Notably, there is norequirement for the vectors to have different magnitudes of theirx-components when using the algorithm based on directionally opposedvectors.

As shown in FIG. 3B, and in accordance with the algorithm employingdirectionally opposed vectors, a plurality of paired sets of two vectorsare established at different points along the x-dimension of a growthcurve. Each of the vectors of a single set of vectors shares the sameorigin (x1,y1). Also as indicated in the figure, the vectors areestablished such that their directions are opposed to each other in thex-dimension. When this is the case, the x-coordinate at the head of thefirst vector (i.e., vector a) has a value less than the value of thex-coordinate at shared origin, and the x-coordinate at the head of thesecond vector (i.e., vector b) has a value greater than the value of thex-coordinate of the shared origin. Stated differently, when usingdirectionally opposed vectors x2<x1<x3, where x1 is the x-coordinate ofthe shared origin, where x2 is the x-coordinate at the head of thevector directed toward decreasing x-values, and where x3 is thex-coordinate at the head of the vector directed toward increasingx-values. This arrangement is distinguished from embodiments of theinvention which employ directionally similar vectors, wherein x1<x2<x3.

Thus, if numerical data representing a growth curve for time-dependentmonitoring of amplicon production in a nucleic acid amplificationreaction is processed by curve fitting to result in an optimizedequation, that equation can be used to parse the processed growth curveinto arbitrary time intervals. For example, these time intervals couldbe 5 seconds each, 10 seconds each, or other desired time or cyclenumber interval. Continuing with this example, the magnitudes of thex-components of the directionally opposed vectors could be arbitrarilyset to 50 seconds. In such a case, the origin of a first paired set ofvectors could be established at x1=50 seconds, the head of the firstvector would then be positioned at x2=0 seconds, and the head of thedirectionally opposed second vector would be positioned at x3=100seconds. As described above, a second paired set of vectors wouldincrement along the x-dimension of the growth curve such that the originof the second paired set of vectors was established at x1=55 seconds,and the process repeated as desired.

The values of the y-coordinates of the vectors preferably are determinedeither directly from experimental data, or more preferably calculatedusing a moving average smoothing function, or a curve fitting operation.When curve fitting is used, values of the y-coordinates of the vectorspreferably are calculated by solving optimized equations usingtechniques described herein, or other techniques that will be familiarto those having an ordinary level of skill in the art. With the x- andy-coordinates of the different paired sets of vectors established, theangles between the vectors can be calculated using standard mathematicalapproaches, such as the above-described Equation (4), and the calculatedangles associated with different time points along the x-dimension ofthe growth curve. In accordance with the algorithm employingdirectionally opposed vectors, determining the time component associatedwith the origin of the vector pair having the minimum angle willidentify the feature of the curve (i.e., the OTArc) to be plottedagainst the input log₁₀ target copy number to create a standard curve,or to be compared with a standard curve to identify the amount orconcentration of polynucleotide analyte in a test sample.

Apparatus for Implementing the Calibration Algorithm

The calibration algorithm disclosed herein is conveniently implementedusing a computer or similar processing device (“computer” hereafter). Indifferent preferred embodiments, software or machine-executableinstructions for performing an algorithm can be loaded or otherwise heldin a memory component of a freestanding computer, or in a memorycomponent of a computer linked to a device used for monitoring,preferably as a function of time, the amount of a product undergoinganalysis. In a highly preferred embodiment, software for executing thecalibration algorithm is held in a memory component of a computer thatis linked to, or that is an integral part of a device capable ofmonitoring the amount of an amplicon present in a reaction mixture as afunction of time.

Indeed, either or both of a controller system for controlling areal-time amplification device and/or the detection system of thereal-time amplification device can be coupled to an appropriatelyprogrammed computer which functions to instruct the operation of theseinstruments in accordance with preprogrammed or user input instructions.The computer preferably also can receive data and information from theseinstruments, and interpret, manipulate and report this information tothe user.

In general, the computer typically includes appropriate software forreceiving user instructions, either in the form of user input into a setof parameter fields, or in the form of preprogrammed instructions (e.g.,preprogrammed for a variety of different specific operations). Thesoftware then converts these instructions to appropriate language forinstructing the operation of the real-time amplification controller tocarry out the desired operation. The computer also is capable ofreceiving data from the one or more sensors/detectors included withinthe system, and interprets the data in accordance with the programming.The system preferably includes software that correlates a feature of agrowth curve representing the quantity of amplified copies of thenucleic acid of interest as a function of time, as detected by thedetector, to the number of copies of the nucleic acid of interestpresent in a test sample.

Preferably, when the computer used for executing the disclosedcalibration algorithm is an integral component of an apparatus forperforming and analyzing real-time nucleic acid amplification reactions,the apparatus preferably comprises a temperature-controlled incubator, adetection device for collecting signals, an analyzing device such as acomputer or processor for analyzing signals and an output device fordisplaying data obtained or generated by the analyzing device. Theanalyzing device may be connected to the temperature-controlledincubator through an input device known in the art, and/or connected toan output device known in the art for data display. In one embodiment,the temperature-controlled incubator is capable of temperature cycling.

Generally speaking, the various components of an apparatus forperforming the real-time nucleic acid amplification useful in connectionwith the disclosed calibration algorithm will be conventional componentsthat will be familiar to those having an ordinary level of skill in theart. The temperature-controlled incubator used to perform and analyzereal-time nucleic acid amplification may be of a conventional designwhich can hold a plurality of reaction tubes. For example, the incubatormay hold up to 96 reaction samples, more preferably up to 384 reactionsamples, or still more preferably up to 1536 reaction samples in atemperature-controlled block in standard amplification reaction tubes orin wells of a multiwell plate. In one aspect, the detection system issuitable for detecting optical signals from one or more fluorescentlabels. The output of the detection system (e.g., signals correspondingto those generated during the amplification reaction) can be fed to thecomputer for data storage and manipulation. In one embodiment, thesystem detects multiple different types of optical signals, such asmultiple different types of fluorescent labels and has the capabilitiesof a microplate fluorescence reader. The detection system is preferablya multiplexed fluorimeter containing an excitation light source, whichmay be a visible light laser or an ultraviolet lamp or a halogen lamp, amultiplexer device for distributing the excitation light to theindividual reaction tubes and for receiving fluorescent light from thereaction tubes, a filtering means for separating the fluorescence lightfrom the excitation light by their wavelengths, and a detection meansfor measuring the fluorescence light intensity. Preferably, thedetection system of the temperature-controlled incubator provides abroad detection range that allows flexibility of fluorophore choice,high sensitivity and excellent signal-to-noise ratio. Optical signalsreceived by the detection system are generally converted into signalswhich can be operated on by the processor to provide data which can beviewed by a user on a display of a user device in communication with theprocessor. The user device may comprise a user interface or may be aconventional commercially available computer system with a keyboard andvideo monitor. Examples of data which can be displayed by the userdevice include amplification plots, scatter plots, sample value screensfor all the tubes or reaction vessels in the assembly and for all labelsused, an optical signal intensity screen (e.g., fluorescent signalintensity screen), final call results, text reports, and the like.

Description of the Algorithm—Creating a Parametric Calibration Curve

Creating a parametric calibration curve begins with a step for forming aplurality of standard samples, each containing a constant quantity of anucleic acid calibrator (i.e., an internal calibrator polynucleotide),and a different known amount of an analyte polynucleotide standard. Forexample, each of the plurality of standard samples could contain 10,000copies of the internal calibrator polynucleotide. The different samplescould also contain known amounts of the analyte polynucleotide standard,for example, with amounts of the standard differing by 10 fold from onesample to the next.

Next, there is a step for coamplifying in a single amplificationreaction the internal calibrator polynucleotide and the analytepolynucleotide standard, and measuring or otherwise determining indiciaof amplification for each of the internal calibrator and analytepolynucleotide in the standard reactions. Generally speaking, theseindicia preferably will be time values required for the amplificationreaction to reach a certain point, or for the amount of ampliconproduced to have reached a particular amount or threshold value. Suchindicia may be measured in cycle numbers for amplification reactionsinvolving thermal or other cycling, or time increments. Indiciarepresenting time increments are preferred for isothermal amplificationreactions that do not involve discrete reaction cycles requiringoperator or machine intervention to promote the amplification reaction.The result of these procedures is a collection of indicia ofamplification for each of the nucleic acid calibrator and analytepolynucleotide as a function of the known starting quantity of analytepolynucleotide standard that was present in the reaction mixture beforethe amplification reaction was initiated.

Of course, the resulting indicia of amplification measured for theamplified analyte polynucleotide standard and amplified internalcalibrator are associated with, or related to the amount of analytepolynucleotide standard input into the reaction. This may be formalizedby graphing, plotting, or more preferably electronically relating: (a)indicia of amplification for reactions conducted using known amounts ofthe analyte polynucleotide standard (Tt), and (b) the amount of analytepolynucleotide standard (S) input into the reaction. Likewise, this mayinvolve graphing, plotting, or more preferably electronically relating:(a) indicia of amplification for the internal calibrator (ICt), and (b)the amount of analyte polynucleotide standard (S) input into thereaction. The individual data points in FIG. 4 represent indicia ofamplification measured for the amplified analyte polynucleotide standardand amplified internal calibrator plotted as a function of the amount ofanalyte polynucleotide standard input into the reaction.

In accordance with the method of creating the calibration curve, therelating procedure or step involves optimizing parametric equations tofit: (1) the indicia of amplification for the amplified analytepolynucleotide standard as a function of the amount of analytepolynucleotide standard input into the reaction, and (2) the indicia ofamplification for the amplified internal calibrator as a function of theamount of analyte polynucleotide standard input into the reaction. Thisconveniently can be accomplished by applying standard mathematicalcurve-fitting techniques to each of the data sets to result in equations(i.e., “fitted equations”) that define curves associated therewith.Thus, equations for each of two different two-dimensional curves can beobtained by this procedure. In one embodiment, a single type of equationis used for describing each of the curves, with each of thetwo-dimensional curves being associated with a different set ofnumerical values for the equation coefficients. The parametric equationused in the curve fitting procedure preferably contains no less thanthree, and more preferably no less than four coefficients that areoptimized or determined during the curve-fitting procedure. Highlypreferred parametric equations have exactly four coefficients, whileother highly preferred parametric equations have exactly fivecoefficients. Optimizing the parametric equation to fit the measuredindicia of amplification can easily be accomplished using a commerciallyavailable software package, such as the SOLVER program which isavailable as an EXCEL add-in tool for finding an optimal value for aformula, and equation solving from Microsoft Corporation, (Redmond,Wash.). The curves generated by this procedure preferably are shapedsuch that increasing levels of the analyte polynucleotide standard inputinto a reaction correlate with reduced indicia of amplification for theanalyte polynucleotide standard plot (e.g., the time-of-emergence isreduced), and correlate with increased indicia of amplification for theinternal calibrator plot (e.g., the time-of-emergence is increased).Indeed, it is generally preferred that the value indicating the indiciaof amplification for the internal calibrator is not substantiallyconstant across the range of input analyte polynucleotide standard (S)values tested in the amplification reactions. The curves drawn in FIG. 4represent the graphical products of fitted parametric equations solvedover a range of values for the known starting amounts of input analytepolynucleotide standard (S), referred to herein as “fitted indicia ofamplification.” Thus, solving the fitted parametric equations atincremental values of the known starting quantity of analytepolynucleotide standard results in fitted indicia of amplification forthe nucleic acid calibrator as a function of the known starting quantityof the analyte polynucleotide standard, and fitted indicia ofamplification for the analyte polynucleotide standard as a function ofthe known starting quantity of the analyte polynucleotide standard.

Although other parametric equations have been used in the curve fittingprocedure with good results, the procedures described below employedconventional four-parameter logistic (“4 PL”) parametric equationshaving the following forms:X=Tt(S)=a _(x) +b _(x)/[1+(S/c _(x))^d _(x)]  (Eq 6)Y=ICt(S)=a _(y) +b _(y)/[1+(S/c _(y))^d _(y)]  (Eq 7)In these equations, Tt(S) represents the indicia of amplification for aknown amount of analyte polynucleotide standard as a function of thestarting amount of analyte polynucleotide standard, and ICt(S)represents the indicia of amplification for the internal calibrator as afunction of the starting amount of analyte polynucleotide standard. Thefour coefficients in these equations that can be optimized by standardprocedures are identified as a_(n)−d_(n). The number of copies ofanalyte polynucleotide standard input into the amplification reaction isidentified by the parameter “S” in the equations. Of course, it is to beunderstood that success in using the method taught herein does notrequire the use of any particular parametric equation. For example,parametric equations based on third-order polynomials were also usedwith excellent results, and fall within the scope of the invention. Yetother contemplated alternatives for curve-fitting include bothnon-linear and linear models, including, but not limited to, regressionanalysis.

Next, there is a step for preparing a three-dimensional parametriccalibration curve. This preferably involves establishing a relationship,such as an electronic representation of a three-dimensional curve,between: (1) indicia of amplification for the analyte polynucleotidestandard (Tt); (2) indicia of amplification for the internal calibrator(ICt), and (3) the amount of analyte polynucleotide standard (S) used inthe reactions yielding these indicia of amplification. In oneembodiment, the result of this procedure is a standard curve plotted ona three-dimensional graph, as illustrated in FIG. 5, where the thirddimension (i.e., the z axis) corresponds to the amount of analytepolynucleotide standard (S) input into the amplification reaction. Ofcourse, such a curve will also have a projection onto the measurementplane, as illustrated in FIG. 5. Each of these related standard curvescan be used for determining the amount of analyte polynucleotide presentin a test sample given only the indicia of amplification measured forthe coamplified analyte polynucleotide and internal calibrator.

Description of the Algorithm—Using the Calibration Curve

Steps for using a space calibration curve are now described.

First, there is a step for forming at least one test reaction mixturecontaining the same known starting quantity of nucleic acid calibratorpolynucleotide that was present in each of the standard samples used tocreate the standard curve, and an unknown starting quantity of theanalyte polynucleotide that is to be quantified.

Next, there is a step for coamplifying, in a single amplificationreaction, the nucleic acid calibrator and any of the analytepolynucleotide that may be present in the test reaction mixture, andmeasuring or otherwise determining indicia of amplification for thenucleic acid calibrator and analyte polynucleotide contained in the testreaction mixture. As above, these indicia can be time values requiredfor the amplification reaction to reach a certain point, or for theamount of amplicon produced to reach a particular amount or thresholdvalue. Such indicia may be measured in cycle numbers for amplificationreactions involving thermal or other cycling steps, or time increments.Indicia representing time increments are preferred for isothermalamplification reactions that do not involve discrete reaction cyclesrequiring operator or machine intervention to promote the amplificationreaction.

Next, there is a step for relating, plotting or specifying (e.g.,electronically specifying) in the x-y plane (i.e., the “measurementplane”) of the three-dimensional parametric calibration curve thecoordinates of the indicia of amplification measured for the coamplifiedanalyte polynucleotide and internal calibrator in the test reaction.This relationship in the measurement plane of the three-dimensionalcalibration curve can be used for determining the amount of analytepolynucleotide contained in a test sample.

Finally, there is a step for determining the value of the parameter Sthat gives the minimum distance between the coordinates for the testsample in the measurement plane and the calibration curve projection inthe measurement plane. Stated differently, this step involves performingcalculations that vary the value of the parameter S to minimize themagnitude of the difference between the coordinates for the test samplein the measurement plane and the calibration curve projection in themeasurement plane. The amount of target present in the test sample isestimated as the value of the parameter S which provides this minimumdistance. This can be accomplished by using the Euclidean norm, asdescribed above, and an iterative computing process.

Application of the Calibration Method to Quantitation of AnalytePolynucleotides

The following Example demonstrated the interdependence betweenproduction of analyte amplicons and internal calibrator amplicons in areal-time nucleic acid amplification system. In this system the internalcalibrator copy number was held constant, and the number of copies ofthe analyte polynucleotide standard was varied. While thetranscription-associated amplification method employed in thisillustration used the combination of one primer having a 3′-endextendable by a DNA polymerase and one T7 promoter-provideroligonucleotide having a blocked 3′-end that could not be extended by aDNA polymerase (essentially as described by Becker et al., in publishedU.S. patent application Ser. No. 11/213,519), the parametric calibrationmethod described herein can also be used with essentially any other invitro nucleic acid amplification system, including those employingpaired sets of oppositely disposed primers having 3′-ends extendable bya DNA polymerase. Indeed, competitive amplification systems resultingfrom coamplification of analyte polynucleotide and internal calibratorusing a shared set of amplification oligonucleotides or primers giveexcellent results with the parametric calibration method disclosedherein, and so represent a category of preferred amplificationreactions. Fluorescence emission results gathered as a function ofamplification reaction time were processed using a mathematicalalgorithm for determining the point at which the fluorescent signalexceeded a pre-determined threshold, sometimes referred to as the“time-of-emergence” above background. The nature of this processing stepis not considered critical, and many alternative processing approachescan be used for determining a point on the growth curve. Examples ofmethods of determining time-dependent indicia of amplification includeTTime, which is described in U.S. patent application Ser. No. 60/659,874at pages 110-116, and TArc and OTArc, which are both described in U.S.patent application Ser. No. 11/474,698, and others. To illustrate theinvented parametric calibration algorithm, the time-dependentfluorescence results obtained in the following Example were processed bythe TTime algorithm for determining time-dependent indicia ofamplification.

Example 1 describes a procedure wherein known numbers of an analytepolynucleotide standard were coamplified in a single amplificationreaction with known, constant numbers of an internal calibratorpolynucleotide. In this Example the analyte polynucleotide standard andthe internal calibrator were amplified using different amplificationoligonucleotides. An alternative arrangement wherein each of thepolynucleotides amplifies using a shared set of amplificationoligonucleotides in a competitive amplification format also has beenused with very good results, and represents a preferred embodiment.

Example 1 Time-Dependent Monitoring of Analyte and Internal CalibratorAmplicon Synthesis

HIV-1 subtype B and nucleic acid calibrator sequences were amplifiedusing a transcription-associated amplification method as described inU.S. patent application Ser. No. 11/213,519. Time-dependent synthesis ofHIV-1 analyte polynucleotide amplicons and internal calibrator ampliconswas monitored using distinguishable molecular torch hybridizationprobes. In these procedures the two multiplexed amplification reactionsdid not share either primers or probes in common. Thus, the HIV-1 targetwas amplified using a T7-provider oligonucleotide, a non-T7 primer, ablocker oligonucleotide, and detected using molecular torch, where eachof these was specific for the HIV-1 target and not the nucleic acidcalibrator. Likewise, the internal calibrator was amplified using aT7-provider oligonucleotide, a non-T7 primer, a blocker oligonucleotide,and detected using a molecular torch, where each of these was specificfor the nucleic acid calibrator and not the HIV-1 target. Amplificationreactions were carried out at constant temperature (i.e., withoutthermal cycling), and amplicon formation was monitored by fluorescenceemission as a function of time. Signals produced by the differenthybridization probes were distinguishable from each other by theirfluorescent emission spectra. All reactions included 30,000 copies ofthe internal calibrator, and were performed in replicates of twelve. Thenumber of copies of HIV-1 target ranged from 0-500,000 copies/reaction.Amplification reactions and detection steps were carried out using aCHROMO4 REAL-TIME DETECTOR instrument (MJ Research/Bio-Rad Laboratories,Inc.; Hercules, Calif.). Time-dependent fluorescent signals proportionalto the extent of amplicon synthesis were normalized to a maximumrelative fluorescence unit (RFU) of one. Fluorescence readingsindicating the amount of amplicon present in the reaction mixture weretaken approximately every 20 seconds. TTime values indicating thetime-of-emergence of the fluorescent signal above a background thresholdfor the different targets were determined essentially as disclosed inU.S. patent application Ser. No. 60/659,874.

Results from the amplification reactions were collected and processedusing different mathematical approaches for comparison. Graphic plots offluorescence signals against reaction time (i.e., real-time run curves)for analyte polynucleotide showed strong evidence for overlap in sampleshaving amounts of analyte polynucleotide that differed by up to 10 fold.Thus, the run curves for reactions conducted using 10 copies of theanalyte polynucleotide were somewhat interspersed with run curves forreactions conducted using 50 copies of the analyte polynucleotide, etc.This variation was quantitatively reflected by the relatively highstandard deviation values appearing in Table 1. Generally speaking,reactions initiated using higher levels of the analyte polynucleotidestandard characteristically suppressed internal calibrator ampliconsynthesis when compared with reactions initiated using lower levels ofanalyte polynucleotide standard. More specifically, and as summarized inTable 1, fluorescent signals representing production of HIV-1 analytepolynucleotide amplicons yielded TTime values ranging from as short as9.9 minutes for the highest level of target tested, to as long as 23.2minutes for the lowest level of target tested. The TTime valuesdetermined for the internal calibrator ranged from as short as 15.43minutes to as long as 27.59 minutes.

TABLE 1 Summarized Quantitative Results from Nucleic Acid AmplificationReactions Internal Calibrator Input Analyte Polynucleotide Standard #Reactions log₁₀ # Reactions Avg Std Dev detecting Avg Std Dev copies ofdetecting TTime TTime internal TTime TTime analyte analyte (minutes)(minutes) calibrator (minutes) (minutes) 0 0 N/A N/A 12 15.43 0.33 1 623.2 2.26 12 15.97 0.46 1.7 12 17.7 1.51 12 15.80 0.30 2.7 12 15.0 0.6212 16.61 0.37 3.7 12 13.1 0.38 12 19.18 0.29 4.7 12 11.9 0.50 12 22.890.33 5.7 12 9.9 0.45 12 27.59 0.32

The following Example illustrates how plotting time-dependent indicia ofamplification as a function of the input analyte polynucleotide copynumber graphically confirmed the inverse relationship between kineticprofiles for the analyte polynucleotide and internal calibratoramplification reactions. As described below, the time-dependent indiciaof amplification for the HIV-1 analyte polynucleotide standard decreasedas a function of increasing amounts of input analyte polynucleotide,while the time-dependent indicia of amplification for the internalcalibrator continuously increased. This confirmed a stronginterdependence between the amount of analyte polynucleotide present inthe reaction mixture prior to the start of amplification and thetime-dependent indicia of amplification for both the analytepolynucleotide and the internal calibrator. Further illustrated is acurve-fitting procedure which resulted in a set of optimized parametricequations describing fitted curves.

Example 2 illustrates the inverse relationship between amplificationprofiles for analyte polynucleotide and internal calibrator, as well asthe use of curve-fitting techniques to obtain parametric equationsfitting experimental results. A subsequent Example describes use of theobtained equations for constructing a three-dimensional calibrationcurve.

Example 2 Relating Time-Dependent Indicia of Amplification to theAmounts of Analyte Polynucleotide Standard Input into AmplificationReactions

Numerical values for the time-dependent indicia of amplification (i.e.,TTime values) determined for the synthesis of analyte polynucleotidestandard and internal calibrator amplicons obtained in the amplificationreactions of the preceding Example were entered into an electronicspreadsheet and visualized in a two-dimensional graphic format havingthe amount of input analyte polynucleotide standard (e.g., measured inlog₁₀ copies) on the x-axis, and time-dependent indicia of amplificationfor each of the amplified targets on the y-axis. Next, standardprocedures familiar to those having an ordinary level of skill in theart were used to fit curves to the measured data points. This involvedoptimizing parametric equations to minimize deviation between a fittedcurve and the measured data. Different approaches were used forestablishing these relationships in a quantifiable manner, and differentmodel parametric equations can be used in the curve-fitting procedure.The technique was particularly illustrated using a general equationexpressed as a function of the parameter S, where S was the amount ofinput analyte polynucleotide standard. Treating the analytepolynucleotide and internal calibrator data sets separately, numericalvalues for a_(n)−d_(n) in Equations 6-7 were optimized usingcommercially available SOLVER software which is available as an EXCELspreadsheet software add-in tool from Microsoft Corporation (Redmond,Wash.). The results of this operation were two equations, each having afixed set of optimized coefficients (a_(n)−d_(n)) that defined curvesfitted to the measured time-dependent indicia of amplification for theanalyte polynucleotide and internal calibrator, respectively. Theseequations had the forms:X=Tt(S)=a _(x) +b _(x)/[1+(S/c _(x))^d _(x)]  (Eq 6)Y=ICt(S)=a _(y) +b _(y)/[1+(S/c _(y))^d _(y)]  (Eq 7)Two-dimensional plots of the data points representing time-dependentindicia of amplification, expressed as TTime values, as a function ofthe amount of input analyte polynucleotide, together with fitted curvesrepresenting solutions to the optimized parametric equations arepresented in FIG. 4.

The following Example describes the establishment of a three-dimensionalrelationship between: (1) time-dependent indicia of amplification forthe analyte polynucleotide standard (Tt); (2) time-dependent indicia ofamplification for the internal calibrator (ICt), and (3) the amount ofpolynucleotide standard (S) used in the reactions which yielded thesetime-dependent indicia.

Example 3 illustrates the preparation of a three-dimensional parametriccalibration curve.

Example 3 Establishing a Parametric Calibration Curve in ThreeDimensions

An electronic spreadsheet created using MATLAB software (The MathWorks;Natick, Mass.) was employed to establish a three-dimensional calibrationcurve using the equations defining fitted curves, as described in theprevious Example. Three functions used for establishing thisrelationship were: (1) time-dependent indicia of amplification for theanalyte polynucleotide standard as a function of the amount of analytepolynucleotide standard input into the reaction; (2) time-dependentindicia of amplification for the internal calibrator as a function ofthe amount of analyte polynucleotide standard input into the reaction;and (3) a mathematical function relating the amount of analytepolynucleotide standard in the z-dimension. Three axes of a graphic plotused to display the calibration curve were assigned as follows:X=Tt(S)=a _(x) +b _(x)/[1+(S/c _(x))^d _(x)]  (Eq 6)Y=ICt(S)=a _(y) +b _(y)/[1+(S/c _(y))^d _(y)]  (Eq 7)Z=Z(S)=log₁₀(S)  (Eq 8)By varying the value of S in the z-dimension, solving for the respectivevalues of x and y, and then graphically displaying the result there wasestablished a three-dimensional calibration curve shown in FIG. 5. Thisthree-dimensional curve represents the relationship between: (1)measurable indicia of amplification in reactions that coamplify variableamounts of an analyte polynucleotide and a constant amount of aninternal calibrator; and (2) the amount of analyte polynucleotidestandard present in the reaction mixture at the start of theamplification reaction. Because the x-y plane of the three-dimensionalplot relates the measurable indicia of amplification for analytepolynucleotide and internal calibrator to each other, this plane isreferred to as the “measurement plane.” Also shown in FIG. 5 is aprojection of the three-dimensional calibration curve onto thetwo-dimensional measurement plane. The two-dimensional relationship,either in electronic spreadsheet form or graphical form, correspondingto the measurement plane in the figure can alternatively be produced bysolving the fitted parametric equations for Tt(S) and ICt(S) over arange of values for the input amount of analyte polynucleotide standard(S) and then graphing or electronically representing the results. Thethree-dimensional standard curve and the two-dimensional curve in themeasurement plane can be used for determining the amount of analytepolynucleotide present in a test sample given the time-dependent indiciaof amplification measured for the coamplified analyte polynucleotide andinternal calibrator.

Example 4 describes evidence that the parametric calibration methodimproved both the precision and accuracy of analyte polynucleotidequantitation. This conclusion was based on analysis of results obtainedin the preceding Examples.

Example 4 Parametric Calibration Method Improved Quantitation of AnalytePolynucleotides Using a Real-Time Nucleic Acid Amplification Protocol

Statistical analysis of results from the above-described nucleic acidamplification reactions was used to assess improvements to precision andaccuracy of calibration curves resulting from application of theparametric calibration method. Values determined in Example 1 for theindicia of amplification for the HIV-1 analyte polynucleotide as afunction of the amount of input analyte polynucleotide in the reactionswere used to establish a line of best fit by a conventional linear leastsquares curve fitting procedure. The average number of log₁₀ copies ofthe HIV-1 analyte, the standard deviation of the number of log₁₀ copiesof HIV-1 analyte, and the average log₁₀ copy difference determined fromthe line of best fit were calculated to assess the quality of theresulting calibration plot in the absence of any adjustment usinginternal calibration. Parallel determinations were made using indicia ofamplification determined for both the analyte polynucleotide andinternal calibrator, and the parametric calibration curves shown in FIG.5 which relate (a) TTime values for amplification of analytepolynucleotide, (b) TTime values for amplification of internalcalibrator polynucleotide, and (c) the number of copies of analytepolynucleotide input into the reactions. A summary of this informationis presented in Table 2.

TABLE 2 Analyte Polynucleotide Quantitation was Improved by theParametric Calibration Method No Internal Calibration AdjustmentParametric Calibration Adjustment Input Analyte Analyte log₁₀ AnalyteAnalyte Std Avg log₁₀ Analyte Analyte Std Avg log₁₀ copies of Avg log₁₀Dev log₁₀ copy Avg log₁₀ Dev log₁₀ copy analyte copies copy differencecopies copy difference 0 N/A N/A N/A N/A N/A N/A 1 −1.48 1.20 −2.48 1.000.33 0.00 1.7 1.45 0.80 −0.25 1.94 0.36 0.25 2.7 2.92 0.33 0.23 2.730.12 0.04 3.7 3.92 0.20 0.22 3.69 0.04 −0.01 4.7 4.57 0.27 −0.13 4.650.05 −0.05 5.7 5.63 0.24 −0.07 5.71 0.07 0.01

The results presented in Table 2 confirmed that the parametriccalibration method substantially improved quantitation of analytepolynucleotides using time-dependent monitoring of in vitro nucleic acidamplification reactions. Ideally, the numbers appearing in the columnsmarked “Analyte Std Dev log₁₀ copy” should be as low as possible. Thevalues in these columns represent the standard deviation of thecalculated analyte log₁₀ copy number, and so relate to assay precision.Comparing the entries in columns three and six reveals that theparametric calibration method uniformly yielded advantageously lowerstandard deviation, and so reflected improved assay precision. Alsoideally, the numbers appearing in the columns marked “Analyte Avg log₁₀copy difference” should be as close to zero as possible. The values inthese columns represent the ability to predict the analytepolynucleotide log₁₀ copy number accurately. Comparing the entries incolumns four and seven, it was clear that the parametric calibrationmethod yielded improved accuracy in the quantitation at all analytepolynucleotide copy levels, except for the 50 copy entry which wasessentially the same for both data processing algorithms. Overall, theinformation in Table 2 indicated that the parametric calibration methodimproved precision and accuracy of analyte polynucleotide quantitation.

The following Example describes amplification reactions that containedknown amounts of analyte polynucleotide, and that were purposelyinhibited to assess the value of the parametric calibration method.These procedures also involved processing time-dependent fluorescencereadings using three different curve analysis algorithms. The firstalgorithm involved the threshold-based determination of the TTime, asdescribed in the foregoing Examples. The second and third curve analysisalgorithms involved determination of the TArc and OTArc values, neitherof these determinations requiring assessment of a baseline level offluorescence or a threshold of fluorescence used for determining indiciaof amplification.

Example 5 describes comparative evidence showing that the parametriccalibration method was useful for quantifying the amount of analytepolynucleotide contained in samples exhibiting inhibition ofamplification. Results showed that the improvement was independent ofthe curve analysis algorithm used to establish the indicia ofamplification.

Example 5 Parametric Calibration Method Improves Quantitation of AnalytePolynucleotides in Test Samples Exhibiting Inhibited Nucleic AcidAmplification

Three-dimensional parametric calibration curves (e.g. as shown in FIG.5) were prepared using the procedures described in the foregoingExamples, except that the same data sets were processed in parallel toidentify as indicia of amplification using different curve analysisalgorithms. Amplification reactions used for preparing the parametriccalibration curves were not purposely inhibited. Amplification reactionsfor experimental test samples were prepared to contain known amounts ofthe HIV-1 analyte polynucleotide in combination with 30,000 copies ofthe unrelated internal calibration polynucleotide. Test sample reactionswere supplemented to contain 5-20% by volume of a HEPES-based washbuffer to inhibit efficiency of the subsequently performedtranscription-associated amplification reaction. Amplification reactionswere performed as described in the foregoing Examples, and fluorescencereadings proportional to amplicon production were monitored as afunction of reaction time for both analyte and internal calibratorpolynucleotides. All reactions were carried out in replicates of ten.The resulting data sets were processed in parallel to identify indiciaof amplification using TTime, TArc, and OTArc algorithms. Amounts ofanalyte polynucleotide contained in the inhibited test samples werecalculated by two different methods. In the first approach, amounts ofanalyte polynucleotide were estimated without using internal calibrationdata. These determinations involved only the indicia of amplificationdetermined for the analyte polynucleotide contained in the test sample,and a linear fit of the indicia of amplification for analytepolynucleotide standard as a function of the amount of input analytepolynucleotide standard for the standard reactions. In the secondapproach, amounts of analyte polynucleotide were estimated using thethree-dimensional parametric calibration curves and the procedureinvolving minimization of the Euclidian norm separating the experimentaldata point plotted in the measurement plane from the projection of thethree-dimensional parametric calibration curve onto the measurementplane, as described above. In all instances, the indicia ofamplification were consistent, meaning that calibration data preparedusing TTime values were used for assessing the amount of analytepolynucleotide in the test sample using data processed to identify TTimeLikewise, calibration data prepared using TArc and OTArc values wereused for assessing the amount of analyte polynucleotide in the testsample using data processed to identify TArc and OTArc, respectively.Summarized results of these procedures are presented in Tables 3-5.

TABLE 3 Improvement to Quantitation of Analyte Polynucleotide UnderConditions of Inhibited Amplification (TTime Analysis) No InternalCalibration Adjustment Parametric Calibration Adjustment Input WeightedWeighted Weighted Weighted log₁₀ % Wash Data Std Dev Avg log₁₀ Std DevAvg log₁₀ Data Std Dev Avg log₁₀ Std Dev Avg log₁₀ copies buffer pointslog₁₀ copy log₁₀ copy points Adj log₁₀ copy log₁₀ copy analyte inhibitorused copy difference copy difference ‡ used copy difference copydifference ‡ 3.0 5 10 0.27 −0.50 2.66 4.97 10 0.20 −0.36 2.05 3.61 4.0 510 0.04 −0.38 0.39 3.84 10 0.06 −0.22 0.64 2.17 5.0 5 10 0.04 −0.46 0.444.59 10 0.07 0.38 0.71 3.77 3.0 10 10 0.37 −1.41 3.68 14.07 10 0.26−1.02 2.56 10.20 4.0 10 10 0.08 −0.75 0.79 7.54 10 0.11 −0.57 1.07 5.755.0 10 10 0.07 −0.88 0.75 8.79 10 0.04 0.55 0.43 5.54 3.0 20 5 0.15−2.69 0.73 13.43 5 0.08 −1.82 0.42 9.11 4.0 20 10 0.13 −2.19 1.30 21.9210 0.10 −1.86 0.96 18.61 5.0 20 10 0.05 −2.09 0.51 20.90 10 0.03 1.100.34 11.02 ‡ absolute value

TABLE 4 Improvement to Quantitation of Analyte Polynucleotide UnderConditions of Inhibited Amplification (TArc Analysis) No InternalCalibration Adjustment Parametric Calibration Adjustment Input WeightedWeighted Weighted Weighted log₁₀ % Wash Data Std Dev Avg log₁₀ Std DevAvg log₁₀ Data Std Dev Avg log₁₀ Std Dev Avg log₁₀ copies buffer pointslog₁₀ copy log₁₀ copy points Adj log₁₀ copy log₁₀ copy analyte inhibitorused copy difference copy difference ‡ used copy difference copydifference ‡ 3.0 5 10 0.27 −0.52 2.71 5.22 10 0.19 −0.21 1.90 2.09 4.0 510 0.05 −0.50 0.54 5.01 10 0.03 −0.39 0.33 3.90 5.0 5 10 0.05 −0.51 0.465.05 10 0.12 0.19 1.16 1.87 3.0 10 10 0.40 −1.50 4.00 14.96 10 0.27−0.77 2.73 7.69 4.0 10 10 0.06 −0.89 0.63 8.95 10 0.06 −0.56 0.62 5.635.0 10 10 0.07 −1.00 0.68 9.99 10 0.14 −0.03 1.36 0.25 3.0 20 5 0.18−2.91 0.92 14.56 5 0.12 −1.42 0.61 7.09 4.0 20 10 0.11 −2.50 1.11 25.0110 0.09 −1.40 0.93 14.01 5.0 20 10 0.10 −2.32 1.00 23.23 10 0.16 −0.471.60 4.70 ‡ absolute value

TABLE 5 Improvement to Quantitation of Analyte Polynucleotide UnderConditions of Inhibited Amplification (OTArc Analysis) No InternalCalibration Adjustment Parametric Calibration Adjustment Input WeightedWeighted Weighted Weighted log₁₀ % Wash Data Std Dev Avg log₁₀ Std DevAvg log₁₀ Data Std Dev Avg log₁₀ Std Dev Avg log₁₀ copies buffer pointslog₁₀ copy log₁₀ copy points Adj log₁₀ copy log₁₀ copy analyte inhibitorused copy difference copy difference ‡ used copy difference copydifference ‡ 3.0 5 10 0.27 −0.52 2.73 5.22 10 0.17 −0.17 1.68 1.72 4.0 510 0.06 −0.50 0.58 5.01 10 0.04 −0.41 0.36 4.07 5.0 5 10 0.05 −0.51 0.475.05 10 0.10 0.14 1.00 1.41 3.0 10 10 0.40 −1.50 4.03 14.96 10 0.23−0.61 2.34 6.14 4.0 10 10 0.07 −0.89 0.67 8.95 10 0.06 −0.54 0.64 5.395.0 10 10 0.06 −1.00 0.61 9.99 10 0.12 −0.09 1.19 0.91 3.0 20 5 0.19−2.91 0.93 14.56 5 0.10 −0.98 0.52 4.91 4.0 20 10 0.12 −2.50 1.15 25.0110 0.09 −1.13 0.85 11.31 5.0 20 10 0.10 −2.32 1.02 23.23 10 0.12 −0.481.23 4.79 ‡ absolute value

A normalized ranking system was used to verify the parametriccalibration method improved analyte polynucleotide quantitation whenamplification reactions exhibited inhibition. Additionally, thisassessment allowed comparison of the relative effectiveness of differentmethods of determining indicia of amplification useful in conjunctionwith the parametric calibration method. This ranking system involvedfirst determining the number of trials to be included in the analysis(i.e., summing the columns identified as “Data points used” in Tables3-5). Next, the sums of the “Weighted Std Dev log₁₀ copy” columns ineach table were determined and then divided by the number of trialsincluded in the analysis. This gave a weighted measure of assayprecision. Next, the sums of the absolute value of the “Weighted avglog₁₀ copy difference” columns in each table were determined and thendivided by the number of trials included in the analysis. This gave aweighted measure of assay accuracy. The calculated weighted measures ofassay precision and accuracy were multiplied, and the resulting productmultiplied by 100 to obtain a single value reflecting a composite scorefor precision and accuracy. An ideal score in this assessment would bezero. Results of these calculations are presented in Table 6. Alsopresented in the table is an indicator of the magnitude of improvementdue to the calibration adjustment. This value was determined bysubtracting from the assay quality score for unadjusted condition theassay quality score for the adjustment by the parametric calibrationmethod, and then dividing the difference by the assay quality score forunadjusted condition. In the example wherein the indicia ofamplification were determined by the TTime algorithm, the improvementscore was calculated as (15.59-8.87)/15.59. An improvement score of zerowould indicate no improvement, while an ideal improvement score would beone.

TABLE 6 Parametric Calibration Method Improves Analyte Quantitation inInhibited Samples Using Different Curve Analysis Algorithms Adjustmentby No Parametric Improvement Adjustment Calibration Method Score RunCurve TTime 15.59 8.87 0.43 Analysis TArc 18.68 7.34 0.61 AlgorithmOTArc 18.89 5.52 0.71

The ranking information summarized in Table 6 confirmed that each ofthree different methods of determining indicia of amplification for theanalyte polynucleotide and internal calibrator gave good results whenused in conjunction with the parametric calibration method to quantifyanalyte polynucleotides, even when amplification reactions weresubstantially inhibited. The final column in Table 6 indicates therelative improvement to assay quality among the different methods ofdetermining indicia of amplification. Entries closer to a value of 1.0indicate increasingly better levels of improvement. As will be drawnfrom Table 6, the two run curve analysis algorithms (i.e., TArc andOTArc) that did not involve determining the time at which a run curveexceeded an arbitrary threshold yielded the greatest improvement.Notably, when the above analysis is limited to results from grosslyinhibited samples (i.e., corresponding to reactions containing 20% washbuffer), the improvement scores resulting from use of the parametriccalibration method are even more dramatic.

While the present invention has been described and shown in considerabledetail with reference to certain preferred embodiments, those skilled inthe art will readily appreciate other embodiments of the presentinvention. Accordingly, the present invention is deemed to include allmodifications and variations encompassed within the spirit and scope ofthe appended claims.

1. A system for quantifying an analyte nucleic acid that may be presentin a sample undergoing testing, comprising: an apparatus that amplifiesnucleic acids and performs time-dependent monitoring of ampliconproduction, said apparatus comprising a temperature-controlled incubatorand an optical detector; a computer operably linked to said apparatus,said computer being programmed to execute the steps of (a) processingresults from a test amplification reaction carried out with a testreaction mixture that comprises an internal calibrator and said sampleundergoing testing, whereby there is generated a test sample data pointcomprising first and second coordinates respectively determined bytime-dependent indicia of amplification for said analyte nucleic acidand said internal calibrator that coamplified in said test amplificationreaction; (b) comparing said test sample data point with a calibrationcurve to locate a point thereon that comprises first and secondcoordinates, and that is minimally distant from said test sample datapoint in a measurement plane that comprises said calibration curve andsaid test sample data point, wherein said calibration curve comprises(i) first dimension coordinates comprising solutions to a firstoptimized parametric equation that specifies time-dependent indicia ofamplification for an analyte polynucleotide standard as a function ofthe parameter representing the known starting quantity of said analytepolynucleotide standard in each of a plurality of calibration reactionsthat comprise said internal calibrator and known starting quantities ofsaid analyte polynucleotide standard, and (ii) second dimensioncoordinates comprising solutions to a second optimized parametricequation that specifies time-dependent indicia of amplification for saidinternal calibrator as a function of the parameter representing theknown starting quantity of said analyte polynucleotide standard in eachof said plurality of calibration reactions, and (c) determining a valuefor the parameter representing the known starting quantity of saidanalyte polynucleotide standard that results in said point located onsaid calibration curve, whereby said value estimates the quantity ofsaid analyte nucleic acid in said sample undergoing testing.
 2. Thesystem of claim 1, wherein said computer controls operation of saidapparatus that amplifies nucleic acids and performs time-dependentmonitoring of amplicon production.
 3. The system of claim 1, whereinsaid computer is selected from the group consisting of a freestandingcomputer, and a computer that is an integral component of saidapparatus.
 4. The system of claim 1, wherein said temperature-controlledincubator is configured to maintain a constant temperature duringperformance of nucleic acid amplification reactions.
 5. The system ofclaim 1, wherein said temperature-controlled incubator is configured fortemperature cycling during performance of nucleic acid amplificationreactions.
 6. The system of claim 1, wherein said optical detectordetects fluorescent signals from a plurality of fluorescent labels. 7.The system of claim 1, wherein said temperature-controlled incubator isconfigured to hold a plurality of reaction tubes.
 8. The system of claim1, wherein said temperature-controlled incubator is configured to hold amultiwell plate.
 9. The system of claim 1, wherein said computerreceives an output of said optical detector for data storage andmanipulation.
 10. The system of claim 1, wherein each of said first andsecond optimized parametric equations respectively comprises a pluralityof optimized coefficients.
 11. The system of claim 1, further comprisingan output device controlled by said computer.
 12. The system of claim11, wherein said computer controls operation of said apparatus thatamplifies nucleic acids and performs time-dependent monitoring ofamplicon production.
 13. The system of claim 12, wherein said computeris selected from the group consisting of a freestanding computer, and acomputer that is an integral component of said apparatus.
 14. The systemof claim 12, wherein said temperature-controlled incubator is configuredto maintain a constant temperature during performance of nucleic acidamplification reactions.
 15. The system of claim 12, wherein saidtemperature-controlled incubator is configured for temperature cyclingduring performance of nucleic acid amplification reactions.
 16. Thesystem of claim 12, wherein said temperature-controlled incubator isconfigured to hold a plurality of reaction tubes.
 17. The system ofclaim 12, wherein said temperature-controlled incubator is configured tohold a multiwell plate.
 18. The system of claim 11, wherein said outputdevice comprises a video monitor.
 19. The system of claim 11, whereinsaid output device displays a result generated by said computer.
 20. Thesystem of claim 19, wherein said result comprises either an amount ofsaid analyte nucleic acid or a concentration of said analyte nucleicacid.
 21. The system of claim 11, wherein said computer is selected fromthe group consisting of a freestanding computer, and a computer that isan integral component of said apparatus.